In
te
r
n
ation
a
l Jou
rn
al
o
f Po
we
r
Elec
tron
ic
s an
d
D
r
ive S
y
stem
(IJ
PED
S
)
V
o
l.
10, N
o.
3, S
ep 2019,
pp.
1
3
1
7
~1
3
2
3
ISSN: 2088-
8694,
DOI
:
10.11591
/ijpeds.
v10.
i
3.pp1317-1323
1
3
17
Jou
rn
a
l
h
o
me
pa
ge
:
ht
tp:
//i
a
e
score
.
com
/
j
o
u
r
na
l
s
/
i
n
d
e
x
.
p
hp/IJ
PED
S
Investigation of dis
tributed generation units placement
and
sizing based on voltage stabil
ity c
o
nditi
o
n indic
a
tor (VSCI)
A
r
vi
n
d
R
aj
1
,
Nu
r
Fa
dila
h Ab
A
ziz
2
,
Z
u
haila
Mat
Yasi
n
3
, Nu
r
As
h
id
a S
a
lim
4
1,
2
De
pa
rtme
nt o
f E
l
e
c
t
ric
a
l
Powe
r
En
g
in
e
e
r
in
g
,
U
nive
rsit
i Te
n
a
ga
N
as
io
nal, M
alay
si
a
3,
4
F
acult
y o
f
Ele
ctri
cal E
ng
ineering
, Univ
e
rs
i
t
i
Te
k
n
o
l
og
i
M
A
RA, M
al
a
y
s
i
a
Art
i
cl
e In
fo
ABSTRACT
A
r
tic
le hist
o
r
y
:
Re
ce
i
v
e
d
A
ug
8,
201
8
Re
vise
d F
e
b 2,
201
9
Ac
ce
p
t
ed
M
ar 6
, 2
0
19
Vol
t
age
i
n
stabi
lity
i
n
power
di
stri
but
ion
syst
e
m
s
can
r
esul
t
i
n
voltage
col
l
ap
se
t
h
r
oug
h
o
ut
t
he
g
rid
.
T
oday,
w
it
h
th
e
adv
a
nced
o
f
p
o
w
e
r
g
enerati
o
n
tech
no
log
y
f
rom
ren
e
wabl
e
s
o
u
r
ces,
co
ncerns
o
f
util
ity
co
m
p
an
ie
s
are
m
u
ch
bei
n
g
fo
cus
e
d
on
t
h
e
s
tab
i
lit
y
o
f
t
he
g
ri
d
w
h
en
t
here
i
s
an
i
n
t
eg
rati
on
o
f
di
st
rib
u
ted
g
e
nerati
on
(
DG
)
in
t
h
e
s
ys
tem.
Th
i
s p
a
p
e
r pres
ents
a
stud
y
o
n
D
G
un
its’
placem
ent
and
si
zin
g
i
n
a
rad
i
al
d
i
s
tri
bution
net
w
ork
by
u
s
i
n
g
a
p
r
e
-
developed
i
n
dex
call
e
d
Vol
t
age
St
ability
C
ondi
t
i
on
I
ndex
(
VS
C
I
)
.
I
n
t
h
i
s
pap
e
r,
V
S
C
I
is
u
sed
t
o
d
et
erm
i
ne
D
G
pl
acemen
t
cand
i
d
a
tes
,
w
hile
t
h
e
v
a
l
u
e
of
p
o
w
er
l
o
s
s
e
s
is
u
s
e
d
to
i
dentif
y
th
e
b
e
st
D
G
p
l
acem
ent
.
T
h
e
p
r
op
osed
m
e
th
od
is
t
este
d
on
a
s
tan
d
ar
d
33-b
u
s
radi
al
d
istri
buti
on
net
w
o
rk
a
nd
com
p
ared w
ith
ex
i
st
in
g
E
t
t
e
had
i
a
n
d
A
m
a
n m
e
t
hod
s.
T
h
e
eff
ective
nes
s
o
f
th
e
m
e
th
od
is
p
resen
t
ed
i
n
t
e
rms
o
f
r
ed
ucti
on
i
n
p
o
w
e
r
s
y
stem
l
os
se
s,
maximizat
i
o
n
of system
l
o
adabi
l
i
t
y and voltage
q
uality
i
mprovem
en
t. Results
show
t
hat
VSCI
can
b
e
utilized
a
s
t
h
e
volt
age
stabi
l
i
t
y
ind
i
cat
or
f
or
D
G
pl
acem
e
n
t
in
r
adi
a
l
d
i
s
t
ri
bu
ti
on
po
wer
system.
Th
e
in
teg
r
ati
o
n
of
DG
is
f
o
und
to
i
mprove
v
olt
a
ge
s
tab
ility
b
y
increasi
ng
the
syst
em
l
oa
dabi
li
ty
a
nd
redu
cin
g
t
he
p
o
w
er
l
osses
o
f
t
he
n
et
work.
K
eyw
ord
s
:
D
i
st
r
i
b
u
te
d
ge
ner
a
t
i
o
n
Ma
ximum
loa
d
a
b
il
it
y
Power
losses
Vo
lt
ag
e
st
ab
il
it
y
Vo
lt
ag
e
st
ab
il
it
y
i
n
d
e
x
Co
pyri
gh
t © 2
019 In
stit
u
t
e
of Advanced
En
gi
neeri
n
g
an
d
S
c
ien
ce.
All
rights
res
e
rv
ed.
Corres
pon
d
i
n
g
Au
th
or:
Nur Fadilah
Ab Azi
z,
D
e
pa
rtme
nt
o
f
El
e
c
t
rica
l
P
o
w
e
r Engi
nee
r
i
n
g
,
C
ol
lege
o
f En
gi
nee
r
ing
,
Un
iv
ersit
i
T
enag
a Nasi
on
a
l
(
Un
it
en
),
Jala
n
Ikram-U
n
ite
n,
430
0
0
K
a
j
an
g,
S
ela
n
g
o
r
,
M
a
l
ay
si
a
.
Em
ail:
nfa
d
ila
h@
u
n
i
t
e
n
.edu.
my
1.
I
N
TR
OD
U
C
TI
O
N
D
i
stri
b
u
t
e
d
ge
ner
a
t
i
on
a
t
t
r
ib
ute
s
t
o
ge
ner
a
t
i
o
n
o
f
pow
er
a
t
the
poi
nt
o
f
c
ons
um
p
tio
n
or
t
he
l
oca
t
io
n
of
l
o
a
d
[
1
,
2].
D
i
stri
b
u
te
d
ge
n
e
rat
i
o
n
a
lso
re
fer
s
t
o
sm
al
l
sc
a
l
e
g
en
era
t
i
on
t
h
at
i
s
n
o
t
di
rec
t
ly
c
o
n
n
ect
e
d
t
o
t
h
e
bu
lk d
istrib
u
t
i
o
n s
y
s
t
e
m
and no
n-
c
e
nt
ra
ll
y
di
sp
at
c
h
ed
[
3
]
.
I
n
p
ub
lis
hed w
o
rks, there
a
re a
numbe
r
of d
iffe
rent
t
e
rms
a
n
d
d
e
fi
nit
i
on
s
are
used
f
o
r
t
h
e
d
e
s
cri
p
t
i
on
o
f
d
i
st
ribu
t
e
d
g
e
n
e
r
at
io
n
[4]
.
T
he
t
erm
‘
e
mbed
de
d
gene
ra
ti
o
n
’
is
o
fte
n
u
se
d
in
A
ng
lo-A
m
e
rica
n
co
u
n
trie
s,
‘
di
spers
e
d
g
e
n
e
r
ati
on’
i
s
use
d
by
N
o
r
t
h
A
m
er
i
c
an
c
o
unt
ri
e
s
a
nd
t
h
e
t
erm
‘d
ec
en
t
r
al
i
s
e
d
g
en
era
t
ion
’
i
s
ap
pl
ie
d
i
n
E
ur
ope
a
nd
p
a
r
ts
o
f
A
s
ia
[
4,
5
]
.
T
he
n
am
e
‘dis
t
r
ibu
t
e
d
g
e
n
e
r
at
io
n
(
D
G
)
’
is
r
ecom
m
e
nd
ed
t
o
be
u
s
e
d
a
ll
o
v
e
r
the
w
o
r
l
d
base
d
on
the
li
tera
ture
s
ur
v
e
y
[4,
5].
P
o
w
e
r
gene
rati
on
at
t
he
l
oc
at
i
o
n
o
f
l
oa
d
de
cre
a
ses
t
h
e
loss
e
s
due
t
o
transm
issi
o
n
over
lon
g
d
i
s
ta
nc
es
a
s
w
e
ll
a
s
o
the
r
c
os
ts
a
ss
oc
ia
t
e
d
w
ith
t
he
d
i
s
tri
b
u
t
i
o
n
sys
t
em
s
.
T
he
c
om
ple
x
ity
a
n
d
t
he
i
ne
fficie
n
c
i
e
s
f
ro
m
the
sy
st
ems
a
r
e
al
so
m
in
i
m
i
z
e
d
w
i
t
h
t
h
e
emer
g
e
n
ce
of
DG
[6
].
I
n
man
y
case
s
,
DG
c
a
n
su
ppl
y
el
ect
ri
city
a
t
a
lower
co
st
w
i
t
h
i
m
p
rov
e
d p
o
w
er
r
e
l
ia
bil
i
t
y and
secur
i
t
y
a
n
d
r
es
u
l
t
e
d
t
o
fe
w
e
r
e
nvir
onme
n
t
a
l
issue
s
c
ompa
red
to co
n
v
e
n
t
i
ona
l ge
nera
t
o
r
s
[7]
.
Vo
lt
a
g
e
st
ab
ilit
y
i
s
d
e
f
i
n
ed
a
s
t
h
e
ab
ili
t
y
o
f
a
p
o
w
er
s
y
s
t
e
m
t
o
m
a
in
tai
n
a
c
cept
a
b
l
e
v
o
l
t
a
ge
l
e
v
e
l
s
at
all
b
u
ses
w
i
t
h
in
t
he
s
ys
tem
[8].
T
he
d
e
f
i
n
it
i
on
i
n
cl
u
d
es
t
he
v
o
l
t
age
o
f
b
us
es
u
n
d
e
r
n
orm
a
l
c
o
n
d
it
i
on
a
n
d
a
f
ter
di
st
urba
nce
i
n
t
he
n
e
t
w
o
r
k
.
A
state
of
vol
ta
ge
i
ns
tab
i
l
i
t
y
i
s
e
x
p
er
i
e
nced
i
n
a
sys
t
em
w
hen
t
h
e
r
e
is
a
con
t
in
uou
s or unc
ontr
o
l
l
a
b
le
d
ro
p i
n
the
m
agn
i
t
u
de
of
vo
lt
a
g
e e
it
he
r a
f
ter
a di
s
t
urba
nc
e,
loa
d
i
n
c
r
ea
se o
r
after
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
Int J
Pow
El
ec &
D
ri
S
yst
,
Vol
.
10,
N
o.
3
, Se
p
2
019 : 1317 –
1
3
23
1
318
a cha
nge
o
c
c
ur
s
i
n
o
pera
t
i
n
g
c
on
d
i
t
i
on
s.
V
olta
ge
i
ns
t
a
b
ili
t
y
c
a
n
re
sult
i
n
v
o
lt
ag
e
c
o
ll
a
p
se
t
h
r
ou
gho
ut
t
he
g
rid
,
in
w
h
i
ch
c
ase
t
h
e
v
o
l
t
a
ge
f
a
l
ls
t
o
an
u
na
cc
e
p
ta
b
l
e,
l
ow
v
alue.
Volt
a
g
e
c
o
ll
a
p
se
i
s
a
co
mmo
n
o
c
cu
rre
n
c
e
i
n
pow
er
s
yst
e
m
s
w
hic
h
a
re
h
ea
vil
y
l
oa
de
d,
f
a
u
l
t
e
d
o
r
ha
v
i
n
g
sh
ort
a
g
e
in
r
ea
ctive
pow
er
[
9,
1
0].
The
c
h
a
nge
i
n
vo
lta
ge i
s dire
c
t
l
y
pro
p
o
rti
o
na
l to c
ha
n
g
e
in
l
o
a
d [
11]
.
T
h
e
r
e
l
a
t
i
o
n
o
f
g
r
i
d
v
o
l
t
a
g
e
s
t
a
b
i
l
i
t
y
a
n
d
g
r
i
d
c
o
n
n
e
c
t
e
d
D
G
c
a
n
be
a
nal
y
se
d
i
n
a
m
ul
t
i
t
ude
o
f
met
h
od
s.
A
s
mu
ch
a
s
t
h
e
rea
c
t
iv
e
po
we
r
su
p
p
o
r
t
sou
r
ced
f
ro
m
ca
p
ac
it
or
b
a
nks
c
a
n
b
e
u
t
i
lised
t
o
reduc
e
pow
er
l
oss,
i
nc
orre
ct
p
lac
e
m
e
nt
o
f
the
c
a
p
ac
i
t
ors
ca
n
f
u
r
t
he
r
i
nc
rea
s
e
t
h
e
l
i
ne
l
o
s
se
s
[1
2]
.
Ca
pac
i
tors
a
re
a
l
s
o
una
b
l
e
t
o
s
up
p
o
rt
t
he
n
etw
o
rk
w
i
t
h
r
eal
p
o
w
er
w
h
e
n
t
h
e
si
tua
t
io
n
a
r
ises
.
DG
s
ystem
s
o
f
f
er
a
b
et
t
e
r
o
p
t
i
on
a
s
it ca
n be
u
til
ise
d
to
su
p
por
t th
e gri
d
wi
t
h
bo
t
h r
eal a
n
d
r
eac
t
i
v
e
po
we
r, a
s
lo
ng
a
s th
e
pl
ace
me
n
t
a
n
d
t
h
e
si
z
i
ng
ca
n
be
o
p
t
i
m
all
y
d
e
t
e
r
m
i
ne
d
.
I
nappro
p
r
i
a
t
e
siz
i
ng
a
n
d
l
o
c
a
t
i
o
n
o
f
d
i
s
t
r
i
but
e
d
g
en
era
t
i
o
n
un
it
s
may
al
so
increase
t
he
s
yst
e
m
losses
as
w
ell
as
t
he
o
pe
rating
cos
t
s.
T
h
e
r
e
f
ore,
it
is
n
e
c
e
s
sa
ry
t
o
i
n
ves
tiga
t
e
the
im
pac
t
s
of
D
G
plac
em
ent a
n
d siz
i
ng t
o
the
s
ys
tem
.
N
a
nna
pane
n
i
e
t
a
l
.
pro
v
i
d
e
a
com
p
rehe
nsive
stud
y
t
o
e
val
u
ate
th
e
effect
i
v
ene
s
s
of
v
ari
o
us
P
Q
an
d
Q
V
volta
ge
s
ta
bi
l
ity
i
n
d
ic
es
o
n
u
t
i
l
iz
i
ng
d
i
st
rib
u
t
e
d
ge
nera
tio
n
(D
G
)
uni
t
s
o
p
t
i
m
al
ly
w
it
hi
n
c
e
rta
i
n
l
i
m
its
a
n
d
con
s
trai
n
t
s
[1
3
]
.
The
ind
i
ce
s
ar
e
u
s
e
d
t
o
i
d
e
n
t
i
fy
t
he
w
e
a
k
e
st
b
u
se
s
a
nd
ca
l
c
u
l
a
t
e
the
s
t
ab
i
lit
y
m
a
r
g
in
o
f
a
syste
m
.
The
study
c
o
nc
lu
des
t
h
a
t
Q
V
se
nsi
t
i
v
i
t
y
i
n
dic
e
s
nee
d
t
o
b
e
co
n
s
i
d
e
r
e
d
a
l
ong
wi
t
h
P
V
s
e
n
s
i
tiv
i
t
y
in
dic
e
s
for
t
h
e
alloc
a
t
io
n
of
D
G
s
.
The
stu
d
y
a
ls
o
s
how
s
h
o
w
t
he
s
e
l
ec
tio
n
of
t
h
e
a
pp
ro
p
r
i
a
t
e
vol
t
a
g
e
s
t
a
b
ilit
y
in
de
x
varie
s
d
e
p
en
d
i
n
g
o
n
t
h
e
D
G
b
u
s
m
ode
l
i
n
t
he
s
im
ulat
ion,
e
i
t
h
e
r
a
s
a
P
V
o
r
P
Q
m
o
d
e
l
.
T
h
e
s
t
u
d
y
pro
poses
a
m
o
r
e
direc
t
m
e
t
h
o
d
in
s
ug
ges
ting
Q
V
in
dex
in
a
na
lys
i
ng
vo
lta
ge
s
t
a
b
ili
ty
a
s
Q
V
c
urve
m
e
t
ho
d
doe
s
no
t
requ
ir
e
the
sys
t
em
t
o
be
r
epr
e
sente
d
a
s
a
tw
o-bus
s
yst
em
.
H
o
w
e
ver
,
Q
-V
c
urve
c
ou
l
d
o
n
l
y
be
u
se
d
for
a
system
w
i
t
h
a c
o
n
s
t
a
n
t
p
ower
l
e
v
el,
th
us
i
t
nee
d
s
P-V cur
ve m
eth
od t
o
b
e pe
rform
e
d
as w
ell.
I
n
a
r
esea
rch
by
N
a
hi
lia
a
nd
B
o
u
d
our
,
a
sta
t
ic
p
ow
e
r
f
lo
w
stu
d
y
b
as
e
d
o
n
th
e
a
n
aly
s
i
s
o
f
Dj
an
et
pow
er
s
ys
t
e
m
beha
v
i
o
u
r
in
t
erm
s
o
f
D
G
con
t
rib
u
t
i
on
a
n
d
v
o
lta
g
e
pr
of
ile
e
v
o
l
u
t
i
o
n
in
A
lgeria
[
1
4
].
A
n
ew
vo
lta
ge
s
ta
bi
li
t
y
i
nde
x
is
u
se
d
t
o
i
d
e
ntif
y
t
h
e
w
e
a
k
est
n
o
d
e
in
t
he
s
ys
t
e
m.
T
his
paper
st
a
t
es
t
ha
t
t
h
e
op
t
i
m
a
l
DG
powe
r
f
ac
t
o
r
must
b
e
c
l
o
s
e
r
t
o
t
h
e
p
o
wer
factor
o
f
t
h
e
com
b
i
ne
d
loa
d
c
o
n
t
ribu
t
i
o
n
i
n
or
der
t
o
m
in
im
i
z
e
pow
er
l
osse
s.
T
he
r
esu
l
ts
o
f
th
i
s
r
esea
rch
show
t
ha
t
the
i
n
t
e
gr
at
i
o
n
o
f
D
G
improve
s
the
vo
l
t
a
g
e
pr
ofi
l
e
a
n
d
dec
r
ea
se
s the
tota
l
p
o
w
e
r l
o
ss i
n
th
e
sys
tem
si
gn
ifica
n
t
l
y
. T
h
e
r
e
s
ea
rch
,
h
owev
e
r
,
d
o
e
s
not
c
o
n
sid
e
r
t
h
e
si
zi
ng
and
the
l
o
ca
ti
o
n
of D
G
i
n
t
he
s
t
u
d
y
.
Wa
ng
et
a
l
.
i
nv
e
s
t
i
g
a
t
e
t
h
e
i
mp
a
c
t
o
f
w
ind
po
we
r
on
s
t
a
ti
c
vo
lt
a
g
e
s
t
a
b
il
ity
[
1
5
]
.
T
he
p
ro
bab
i
li
s
t
ic
st
a
t
i
c
v
o
lta
ge s
t
a
b
ili
t
y
of p
o
w
e
r
syst
ems is
a
na
lyse
d base
d on
P
r
obab
i
l
i
st
i
c
Loa
d F
l
ow
(
P
L
F
)
, w
h
ich is
ab
l
e to
take
unce
r
tai
n
f
act
ors
int
o
c
o
n
s
i
dera
ti
on,
f
o
r
e
xa
mple
l
oa
d
d
i
s
t
r
i
but
i
o
n
a
n
d
ra
ndo
mn
ess
o
f
i
np
ut
v
a
r
i
a
bl
es.
Q
u
asi-M
o
n
t
e
Ca
rl
o
(Q
MC)
si
m
u
lat
i
on
u
s
i
ng
S
obo
l
se
q
u
e
nc
e
i
s
a
p
p
l
ie
d
t
o
s
olve
P
LF
a
fte
r
c
on
sid
e
rin
g
t
h
e
rand
om
i
np
u
t
v
a
r
ia
bles,
w
h
il
e
N
a
taf
tra
n
sfo
r
m
i
s
u
se
d
to
m
ana
g
e
t
he
c
o
r
relati
on
o
f
w
i
nd
p
ow
er.
The
r
e
sul
t
s
prese
n
t
e
d
in t
h
i
s
pa
per
ar
e
com
p
are
d
w
it
h
t
h
e
data
g
e
n
e
r
ate
d
f
r
om
M
on
te
-Ca
r
l
o
S
imula
t
i
on
(
M
CS
)
c
o
mbi
n
e
d
w
ith
S
i
m
p
l
e
Ra
nd
om
S
a
m
pli
n
g
m
e
th
o
d
t
o
s
how
t
he
i
m
p
ro
vem
e
nt
m
a
d
e
.
H
o
w
e
ver,
t
he
N
a
t
a
f
t
rans
for
m
a
nd
a
S
obo
l se
que
nc
e
w
h
ich a
r
e
nee
d
ed f
or th
i
s m
e
th
o
d
m
akes
t
h
e
proc
e
ss to be
qui
te te
d
io
us.
A
m
an
e
t
a
l
.
H
a
s
i
n
tro
d
u
ce
d
a
new
i
nde
x
for
the
pla
c
e
m
e
nt
a
n
d
s
i
zi
ng
o
f
DG
uni
ts
[
16
].
T
h
e
a
l
lo
c
a
ti
on
a
nd
s
i
z
i
n
g
of
D
G
un
i
t
s
i
n
th
i
s
r
e
s
e
a
r
c
h
u
si
ng
t
he
p
r
op
ose
d
i
n
d
e
x
is
t
o
de
ter
m
ine
t
h
e
bus
w
it
h
t
h
e
most
v
ol
ta
ge
s
ens
iti
vi
t
y
a
n
d
min
i
mum
t
o
t
a
l
pow
e
r
l
o
s
s
e
s.
T
he
i
n
de
x
,
pow
e
r
s
t
a
b
i
l
i
t
y
i
n
d
ex
(
P
S
I),
i
s
deve
l
ope
d
b
y
t
ak
i
n
g
s
t
ab
le
n
o
d
e
v
o
l
t
a
g
e
i
n
c
on
si
dera
ti
o
n
.
The
s
i
m
ula
t
ion
r
e
s
u
l
t
s
sh
o
w
t
ha
t
the
D
G
u
ni
t
s
impro
v
e
t
h
e
v
o
l
t
a
g
e
profi
l
e
of
t
he
n
e
t
w
o
r
k
a
nd
i
n
c
r
ea
se
t
he
s
y
s
t
e
m
vol
ta
ge
s
ta
b
i
l
ity
.
The
o
v
e
r
al
l
syste
m
c
a
p
a
c
ity
a
lso
in
c
r
ea
se
s
wh
il
e
red
u
c
ing
th
e
l
i
n
e
l
o
s
s
e
s.
T
he
p
ro
p
o
se
d
a
l
gor
it
hm
i
s
fo
u
nd
t
o
c
ons
um
e
less
com
p
u
t
a
t
i
o
n
ti
me
c
om
pare
d
to
t
he
G
ol
de
n
S
e
c
tio
n
S
e
a
r
c
h
(
G
S
S
)
a
l
gori
t
hm
b
y
5
0
-60
%
.
H
o
w
e
ve
r
,
t
he
perform
ance
o
f
t
h
e
tec
hni
que
d
e
p
e
n
d
he
a
v
i
l
y
on
the
in
i
t
i
a
l
g
u
es
s
an
d
t
h
e
al
go
ri
th
m
i
s
d
ev
e
l
op
e
d
w
it
h
se
v
e
ra
l
t
h
eo
ret
i
c
a
l
a
ssu
m
p
tio
ns
s
u
c
h
a
s
c
o
n
t
i
nui
ty
,
c
o
nv
ex
ity
a
nd
d
i
f
f
e
r
e
n
t
i
a
b
i
l
i
t
y
w
h
i
c
h
m
a
y
n
o
t
b
e
s
u
i
t
a
b
l
e
f
o
r
op
tim
iza
t
i
o
n prob
lem
s
.
Base
d
o
n
t
he
litera
ture
r
ev
ie
w
s
,
it
c
a
n
b
e
c
onc
l
ude
d
t
h
a
t
t
h
e
re
a
re
m
any
differ
en
t
in
d
i
c
e
s
used
f
or
vo
lta
ge
s
ta
b
i
l
i
t
y
ana
l
ysi
s
a
s
w
e
l
l
a
s
ma
ny
di
ffe
re
nt
a
p
p
ro
ac
hes
f
o
r
DG
p
l
ac
e
m
en
t
an
d
si
z
i
ng
.
So
me
o
f
t
h
e
vo
lta
ge
s
ta
bi
li
ty
i
n
d
i
c
e
s
are
n
o
t
en
t
i
rely
r
el
i
a
ble
o
n
t
he
i
r
o
w
n
an
d
nee
d
t
o
b
e
calc
u
la
t
e
d
t
oge
t
h
er
w
it
h
ano
t
her
in
de
x f
o
r i
t
t
o be
a
ccur
a
te. Whi
le
mos
t in
d
i
c
e
s are
com
p
ar
ati
v
e
ly re
l
ia
ble
, som
e of
t
he
ap
p
r
o
ac
he
s p
u
rsu
e
d for
the
p
l
ace
me
n
t
a
nd
siz
i
ng
o
f
D
G
a
r
e
too
re
sour
ce
e
x
t
e
nsi
v
e.
A
s
i
mpler
and
less
res
o
urce
e
xt
ens
i
ve
m
eth
o
d
i
s
nee
d
e
d
f
or
t
h
e
v
o
lta
ge
s
t
a
b
i
l
i
t
y
a
na
l
y
s
i
s
i
n
t
he
p
r
e
se
nce
of
D
G
u
n
i
ts.
Th
is
p
a
p
e
r
p
r
e
sen
t
s
t
h
e
a
b
il
it
y
o
f
V
o
l
t
a
g
e
Sta
b
il
ity
C
o
n
d
it
io
n
I
ndic
a
t
o
r
(V
SC
I)
i
n
D
G
pla
c
e
m
ent.
P
r
e
vio
u
sly,
t
he
c
apa
b
i
l
i
t
y
of
V
S
C
I
as
t
h
e
vo
lta
ge s
ta
bi
l
ity ind
ica
t
or
in t
r
a
n
smissio
n
sy
s
te
m has be
e
n
pr
o
ven in [1
7
-20].
In t
h
i
s p
a
p
e
r,
V
S
C
I
is e
valua
t
e
d
in
a
r
ad
ia
l
d
i
str
i
bu
t
i
o
n
s
yst
e
m
ne
t
w
or
k.
T
he
o
b
j
e
c
t
i
v
e
o
f
D
G
in
t
e
gra
t
i
on
i
n
t
his
pa
pe
r
is
t
o
impr
o
v
e
t
h
e
syste
m
l
oa
da
b
i
l
i
t
y
a
nd re
d
u
ce
pow
er
s
yste
m
l
o
sses.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Inv
e
st
i
g
a
t
i
o
n o
f
di
st
r
i
bu
te
d ge
ner
a
ti
on u
n
its
pl
acem
en
t a
nd
siz
i
n
g
b
a
se
d o
n
vol
t
age
… (Nur Fa
di
l
ah A
b
Aziz)
1
319
2.
RESEARCH
M
ETH
O
D
2.1.
V
o
lta
g
e
st
abil
it
y con
d
ition
ind
i
c
a
tor
(VSC
I)
V
S
CI
h
a
s
b
ee
n
pro
p
o
sed
i
n
[
1
7
]
and
is
d
e
r
ive
d
from
t
h
e
c
u
rre
nt
e
qua
t
i
o
n
i
n
a
com
p
le
x
f
o
rm
o
f
a
si
m
p
le
2
-bu
s
Theve
n
i
n
eq
u
i
va
len
t
sys
tem
. F
or
a
t
yp
ica
l
t
ran
s
m
i
s
si
o
n
li
n
e,
V
SCI
can
b
e
c
a
lc
u
l
a
t
e
d
by
1
)
)
sin
cos
2
(
)
(
4
2
2
2
2
2
Th
Th
Th
E
Q
Z
Q
P
Z
VSCI
(
1
)
Whe
r
e,
P
and
Q
=
acti
v
e
and r
eac
t
i
ve
pow
er
load,
∠
=
Th
ev
en
in
vo
l
t
a
g
e
,
∠
= The
v
e
n
in
i
mpeda
n
ce
or
t
h
e
to
ta
l equ
i
va
le
nt
i
m
p
eda
n
ce
ac
ross
t
he b
us,
and
δ
a
nd
β
a
re their
c
orr
e
spo
n
d
i
ng
p
h
ase
an
gle
s
.
I
n
o
rder
t
o
m
a
in
ta
in
t
he
s
ta
b
i
l
i
t
y
o
f
t
h
e
s
y
s
t
e
m
,
VS
C
I
v
a
l
ue
m
u
st
b
e
l
e
ss
tha
n
o
r
eq
ua
l
t
o
one
a
s
in
equa
t
i
o
n
(
1).
A
ny
b
u
s
tha
t
h
as
V
S
C
I
val
u
e
ne
ar
t
o
o
n
e
im
plie
s
t
ha
t
t
h
e
b
u
s
is
a
ppr
oac
h
i
n
g
it
s
c
o
l
l
a
p
s
e
p
oi
n
t
.
Pr
evio
usl
y
,
VS
C
I
h
as bee
n tes
t
e
d
to
b
e
a
bl
e
t
o
e
va
lua
t
e t
h
e vo
l
tage
s
tab
i
lit
y i
n
tra
nsmiss
ion
line
[17-
2
0
]
.
This
pape
r a
i
m
s
to t
e
st
t
he
ca
p
ab
i
lity
o
f V
S
C
I
to e
v
al
ua
te
t
he
vo
l
t
a
ge
s
ta
bi
li
ty
i
n
ra
d
i
a
l
d
istri
b
ut
ion
s
y
ste
m
.
2.2.
D
G p
l
acem
en
t an
d sizi
n
g
b
ase
d
o
n V
S
I
To
da
y,
D
G
s
a
re
u
sed
t
o
i
mpr
ove
t
he
t
r
a
d
i
ti
ona
l
e
l
e
c
tr
ic
p
ow
er
s
ystem
s
[
21-
22].
These
te
ch
n
o
lo
gi
es
inc
l
ude
s
m
a
ll
o
r
m
i
cro
gas
t
u
rb
ines,
fue
l
c
ell
s
,
w
i
n
d
a
n
d
s
o
l
a
r
e
nerg
y,
b
i
o
ma
ss,
sma
l
l
h
ydr
o-p
o
w
e
r
and
ot
hers.
In
o
rde
r
t
o
a
c
h
i
e
v
e
th
e
bene
f
i
ts
o
f
inte
grat
i
ng
D
G
u
n
i
t
s
in
to
t
he
p
ow
er
s
ys
tem
,
a
n
a
ppr
o
p
ria
t
e
plac
e
and
si
ze
o
f
t
h
e
D
G
u
n
its
i
ns
ta
ll
e
d
m
u
s
t
be
s
e
l
ec
ted.
I
ns
ta
l
lin
g
t
he
u
nit
s
a
t
ina
p
pro
p
r
i
a
t
e
p
l
ace
s
ma
y
w
e
a
k
en
the
sta
b
ili
ty
a
nd
re
l
i
a
b
il
i
t
y
o
f
t
he
p
ow
er
s
yst
e
m
[2
3].
I
n
t
h
i
s
p
a
p
e
r
,
th
e
stud
y
is
b
e
i
ng
d
i
v
i
d
ed
i
nt
o
t
w
o
ph
as
e.
In
t
he
f
irs
t
pha
se,
the
c
a
n
d
i
d
a
t
e
l
o
ca
ti
o
n
s
o
f
D
G
uni
ts
i
s
c
h
os
e
n
a
ccor
d
i
n
g
to
V
SCI
val
u
e
.
T
his
p
h
ase
i
s
v
ery
usefu
l
t
o
m
i
n
i
m
i
ze
t
he
s
ize
t
o
b
e
use
d
i
n
t
h
e
o
p
t
im
iza
t
io
n
proc
ess
for
the
second
p
ha
se
e
specially
f
or
v
ery
large
siz
e
o
f
pow
er
s
ys
tem
netw
ork.
S
ec
on
d
l
y,
t
he
b
es
t
l
o
ca
t
i
on
a
nd
s
izi
n
g
of
t
he
D
G
units
a
re
t
he
n
deter
m
i
n
ed
b
a
s
ed
o
n
the
ob
j
e
c
t
i
v
e
func
t
i
on
w
h
i
c
h
ar
e
i
n
t
his
pa
per
t
h
e
a
i
m
i
s
t
o
m
i
n
i
m
i
ze
the
power
l
osse
s
and
ma
xi
m
i
ze
the s
y
stem
lo
a
da
b
ili
t
y
. F
igure
1 (a) show
s the
fl
o
w
c
hart f
o
r
the
f
irst p
has
e
of
t
h
e
st
u
dy.
I
n
t
he sec
on
d p
h
ase o
f
the
s
t
u
dy
as sh
o
w
n
in
F
i
gure 1
(b)
,
t
he
r
a
nk
i
ng
o
f
t
he
w
eake
s
t bu
se
s
ba
se
d on
t
h
e
VSC
I
v
al
ues
are
u
s
ed
t
o
d
e
t
e
rmin
e
t
h
e
b
e
st
p
l
a
c
e
m
e
n
t
o
f
D
G
un
i
t
s to
b
e insta
lled i
n
t
o
the
s
ys
tem
.
The t
o
p
10
w
e
a
k
b
uses
w
it
h
V
S
CI
a
bove
0
.9
5
are
u
s
ed
t
o
plac
e
a
D
G
uni
t
at
eac
h
lo
c
a
t
i
on
a
nd
t
h
e
e
ffe
ct
s
on
t
he
n
e
t
w
o
r
k
po
we
r
lo
sse
s
a
r
e
studi
e
d
.
Th
e
bu
s
t
h
at
g
iv
e
th
e
mini
mu
m
v
a
l
ue
o
f
p
o
w
e
r
l
o
sses
are
c
hos
en
t
o
b
e
t
he
op
tim
al
l
oca
t
i
on.
N
e
x
t
,
t
o
c
a
lcu
l
a
t
e
t
h
e
s
i
ze
of
D
G
un
i
t
t
o
b
e
in
st
all
e
d
,
s
ev
e
r
al
p
arame
t
ers
a
r
e
t
a
k
e
n
in
t
o
ac
cou
n
t
w
hi
c
h
a
re
t
he
D
G
penetra
t
i
o
n
perc
enta
ge
(
P
n
),
pow
er
f
ac
tor
(
p
f)
v
al
ue
o
f
the
s
y
s
t
em
a
nd
n
u
m
be
r
of
D
G
units
(
N
u
m
)
.
I
n
t
h
i
s
pa
per,
t
he
s
iz
e
o
f
D
G
are
dete
rm
ined
b
y
v
a
r
yi
n
g
t
he
p
e
n
et
rati
on
pe
rce
n
t
a
ge
a
n
d
pow
er
f
a
c
t
o
r.
A
s
a
result,
i
n
th
is pape
r
,
the bes
t
p
e
n
e
t
r
a
ti
on
le
vel of
D
G
and
pow
e
r
f
ac
tor
va
lue
o
f
t
he sy
s
tem
ca
n
be
i
de
n
t
i
f
i
e
d.
T
he
t
ype
s
of
D
G
use
d
a
re
m
ade
cons
t
a
nt
w
h
i
c
h
c
an
i
nj
e
c
t
bot
h,
a
cti
v
e
an
d
re
act
ive
power
.
The
va
lue
of
a
ppare
nt
pow
er,
S
,
r
eal
powe
r
,
P
and
r
eac
tive
p
o
wer,
Q
t
o
be
s
u
ppl
ie
d
b
y
t
he
D
G
un
i
t
i
s
ca
l
c
u
l
a
t
e
d
usi
n
g
the
s
t
e
ps
b
e
l
ow
:
a.
The
pe
ne
trat
io
n
le
vel,
a
nd
t
h
e
t
o
ta
l
ap
par
e
nt
l
oa
d,
i
n
t
h
e
ne
tw
ork
is
u
se
d
t
o
c
a
l
c
u
l
a
te
t
h
e
appa
re
nt p
ow
e
r
to be
sup
pl
i
e
d by
the
D
G
unit,
a
s show
n in the
form
u
la
b
elow
:
1
0
0
%
(
2
)
%
(
3
)
b.
The
re
al
pow
e
r
t
o
be
s
up
p
l
ie
d
by
t
h
e
D
G
u
n
i
t
,
i
s
c
a
lc
ul
ated
b
y
usi
ng
t
h
e
va
lue
of
D
G
a
p
p
a
ren
t
pow
er
and
the
pow
e
r
fact
or
s
et for
the
D
G
uni
t
:
(
4
)
c.
The
rea
c
ti
ve p
ow
e
r
to
be sup
pl
ie
d by
the
D
G
unit,
i
s
c
a
l
c
u
l
at
ed
u
si
ng
t
he
f
o
r
mu
l
a
b
el
o
w
:
(
5
)
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
: 208
8-
869
4
Int J
Pow
El
ec &
D
ri
S
yst
,
Vol
.
10,
N
o.
3
, Se
p
2
019 : 1317 –
1
3
23
1
320
d.
The
r
eal
a
n
d
r
ea
cti
v
e
p
o
we
r
to
b
e
s
u
pp
l
i
e
d
by
t
h
e
DG
u
n
it(s)
i
s
d
ivi
d
ed
e
q
u
a
l
l
y
a
mo
ng
t
h
e
nu
mb
er
o
f
un
its t
o
be in
t
e
g
ra
te
d in t
he
n
etw
o
rk
:
(6
)
(7
)
(a)
(
b
)
F
i
g
u
r
e
1
.
F
l
o
w
char
t
of t
he
de
v
e
l
o
p
e
d
al
g
ori
t
hm
f
or; (
a
)
D
G
pla
c
em
en
t,
(b)
D
G
siz
i
n
g
.
3.
RESULT
S
A
N
D
DISCU
SSIO
N
The
sim
u
l
a
tio
n
i
n
th
i
s
pa
per
w
a
s
c
o
mpu
t
ed usin
g
t
he
3
3-
bus
r
a
d
i
a
l
distri
b
u
t
ion
ne
tw
ork
[2
4].
This
i
s
a
ra
dia
l
d
i
s
tri
b
uti
o
n
s
y
ste
m
w
it
h
33
b
u
s
e
s
,
5
tie
line
s
o
r
l
o
o
p
ing
br
anc
h
e
s
.
It
c
o
n
s
i
sts
of
1
g
e
n
e
r
at
or
bus
a
s
a
sw
ing
bus,
32
loa
d
buse
s
a
nd
37
i
n
t
e
r
co
nne
c
tin
g
bra
n
che
s
.
Ta
b
l
e
1
s
ho
ws
t
he
s
yst
e
m
d
e
ta
i
l
s
of
3
3
-
bu
s
ra
d
i
al
di
stri
b
u
t
i
on
n
e
t
w
ork.
Tab
l
e
1. 33-
bus
r
adia
l
d
i
s
t
ri
b
u
t
i
on
system
’s
d
eta
i
ls
T
o
ta
l
Ac
tiv
e
L
o
a
d
in kW
(P
)
To
t
a
l
Re
act
iv
e
Lo
a
d
i
n
k
VAR (
Q)
T
o
ta
l A
ppa
r
e
nt L
oa
d
in
k
V
A
(S
)
Sys
t
e
m
P
o
w
er
Fa
ct
or
(
p
f
)
371
5
2300
4369.
3
5
0.
8502
3.1.
Wea
k
bu
s
es based
on VSCI
I
n
t
h
e
f
i
r
s
t
p
h
a
s
e
o
f
r
e
s
e
a
r
c
h
,
i
n
o
r
d
e
r
t
o
d
e
t
e
r
m
i
n
e
w
e
a
k
b
u
s
s
e
s
,
loa
d
f
or
e
ve
ry
b
usse
d
w
e
r
e
i
n
c
r
ea
sed
u
n
til
th
e
sy
st
em
r
e
a
c
h
e
d
i
t
s
m
ax
i
m
u
m
l
o
a
d
a
b
i
lit
y
li
mi
t.
V
SCI
va
lue
w
a
s
the
n
c
a
l
c
u
l
a
te
d
a
n
d
t
h
e
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Inv
e
st
i
g
a
t
i
o
n o
f
di
st
r
i
bu
te
d ge
ner
a
ti
on u
n
its
pl
acem
en
t a
nd
siz
i
n
g
b
a
se
d o
n
vol
t
age
… (Nur Fa
di
l
ah A
b
Aziz)
1
321
syste
m
w
as
r
a
nke
d
ac
c
o
rd
i
n
g
to
V
S
C
I
va
lue
.
T
he
V
S
C
I
val
u
es
t
ha
t
c
l
o
s
e
t
o
u
n
i
t
y
w
e
r
e
c
o
n
s
i
d
e
r
e
d
a
s
w
e
a
k
bus
es.
Ta
bl
e
2
sh
ow
s
the
ran
k
o
f
t
op
1
0
w
ea
k
b
u
sse
s
a
t
th
e
ma
xi
m
u
m
l
o
a
d
ab
i
l
i
t
y
o
f
t
h
e
syst
em
.
The
r
e
sul
t
s
are
c
onsis
te
nt
w
it
h [25]
and
t
h
e
vo
l
t
age
b
u
s
e
s m
a
gni
tu
des w
h
ic
h
g
i
v
e al
mo
st
th
e
same
wea
k
b
u
s
es
ran
k
i
ng
.
T
a
b
l
e 2.
Top
1
0
bus
se
s w
i
t
h
h
ig
hes
t
V
S
C
I
for m
a
ximum
loa
d
a
b
ili
t
y
B
u
s
No
V
olta
g
e
(
p.
u.
)
V
S
C
I
18
17
16
32
33
31
15
14
30
13
0.
429
0.
4337
0.
4494
0.
4609
0.
4589
0.
4676
0.
4598
0.
4705
0.
4975
0.
4878
0.
9999
0.
9849
0.
9527
0.
9443
0.
9331
0.
9265
0.
9126
0.
8828
0.
8750
0.
8646
R
e
a
l
P
owe
r
L
oss
e
s
(M
W)
7
.
8640
R
e
a
c
tive
Powe
r
L
o
sse
s
(M
VA
R
)
5
.
3385
3.2.
DG p
l
a
cement
a
nd sizing
A
D
G
uni
t
su
p
p
l
y
in
g
bo
t
h
r
ea
l
a
n
d
r
eac
t
i
ve
pow
e
r
w
as
p
la
ce
d
at
eac
h
w
e
ak
b
uses
r
a
nke
d
as
t
he
t
op
t
e
n
b
a
sed
on
V
SCI.
I
n
th
i
s
p
a
p
er,
th
e
t
ype
o
f
DG
u
n
it
s
pl
a
c
e
d
i
n
t
h
e
ne
tw
ork
ca
n
i
n
jec
t
b
ot
h
ac
t
i
v
e
a
nd
rea
c
ti
ve
pow
e
r
.
The
performa
n
ce
o
f
D
G
un
i
t
s
w
i
t
h
d
iffe
rent
o
per
at
ing
p
o
we
r
fa
ct
ors
ar
e
eva
l
ua
te
d
ba
sed
o
n
the
res
u
l
t
i
ng
m
a
ximum
l
o
a
d
a
b
i
lit
y
of
t
he
n
e
t
w
o
rk,
w
h
ich
a
r
e
sh
o
w
n
i
n
Ta
ble
3.
T
he
c
a
l
c
u
la
t
i
o
n
t
o
de
ter
m
ine
am
oun
t
o
f
DG r
eac
t
i
ve
a
nd
ac
t
i
v
e
p
o
wer i
n
je
cted
is as d
iscu
ssed
i
n S
e
ct
i
o
n
2.2. In
t
h
e
be
g
i
n
n
i
n
g
, the
s
ize
w
a
s
set
t
o
4
0
%
p
e
n
etra
tio
n
l
e
vel
(
a
nd
a
t
opera
t
i
n
g
pow
er
f
a
c
t
o
r
of
0
.8
5
[2
5-2
6
].
T
he
n
etw
o
rk
l
oa
da
bi
l
i
t
y
w
as
set
co
ns
tan
t
a
t
3.5,
w
hich
w
as
t
he
m
a
x
im
um
l
oa
d
a
b
i
l
i
t
y
o
f
t
h
e
b
a
s
e
ca
se
n
e
t
wo
rk
.
Th
e
re
al
a
nd
r
ea
c
t
iv
e
pow
er
l
osses
o
f
t
he
s
im
u
l
a
tio
n
co
nd
uc
te
d
w
e
r
e
a
naly
sed.
F
rom
F
i
gure
3
,
t
he
s
ys
t
e
m
h
a
s
t
h
e
low
e
s
t
pow
er
lo
sse
s
w
he
n
a
D
G
uni
t
w
a
s
plac
ed
a
t
b
u
se
s
32,
3
3
an
d
31,
r
espec
tive
l
y.
T
he
refore,
in
t
h
i
s
paper
,
buse
s
32,
3
3
a
n
d
3
1
are
d
e
t
e
rmi
n
ed
a
s
th
e
b
e
st
l
o
cati
o
n
fo
r
t
h
e
DG
p
l
acemen
t
.
Thi
s
r
esu
lt
i
s
c
o
n
sist
e
n
t
w
i
t
h
t
he
f
in
din
g
s
ob
ta
ine
d
i
n [2
5
-
26].
The
siz
e
o
f
D
G
w
a
s
de
t
e
rm
i
n
e
d
by
va
ryi
ng
the
pe
netra
t
i
on
l
e
ve
l
(
o
f
D
G
.
I
n
t
h
i
s
p
a
p
e
r
,
t
h
e
pene
tr
at
ion
le
v
e
l
of
D
G
w
a
s
varie
d
r
an
g
i
n
g
from
2
0%
t
o
80
%,
f
ro
m
o
n
e
u
n
i
t
o
f
D
G
u
p
t
o
t
h
r
e
e
u
n
i
t
s
o
f
D
G
eva
l
ua
t
e
d
i
n
t
he
s
ys
tem
.
B
a
s
ed
on
Ta
ble
3,
it
c
a
n
b
e
s
e
en
t
ha
t
t
h
e
n
e
tw
ork
has
t
h
e
hi
gh
est
m
a
x
i
m
u
m
loa
d
a
b
i
l
ity
w
h
e
n
t
h
e
D
G
uni
t
(
s)
w
e
r
e
oper
a
t
i
ng
a
t
0
.
85
po
w
e
r
fa
ctor.
Thi
s
i
s
due
t
o
the
D
G
ope
rati
ng
pow
er
fa
ct
or
i
s
be
in
g
cl
oser
t
o
the
sys
t
em
p
owe
r
f
a
c
tor,
w
h
i
c
h
i
s
ab
o
ut
0
.8
5
as
t
a
b
ula
t
e
d
i
n
Ta
ble
1.
T
h
i
s
r
e
sul
t
i
s
con
s
is
t
e
nt
w
ith
t
he
f
ind
i
ngs
r
e
por
ted
i
n
[
2
6
]
w
h
i
c
h
s
t
a
t
e
s
t
hat
t
he
m
ax
imum
l
oada
b
i
l
i
t
y
of
t
he
s
ys
tem
w
h
e
n
bei
n
g
i
n
te
gra
t
e
d
w
i
t
h
D
G
ca
n
be
a
c
h
ie
ve
d
w
h
e
n
t
he
D
G
oper
a
t
i
ng
p
o
w
e
r
f
a
c
tor
is
s
im
il
a
r
t
o
t
h
e
s
y
stem
pow
er
f
ac
tor.
T
ab
le
3
a
lso
show
s
tha
t
a
lth
ou
g
h
t
he
s
iz
e
a
n
d
the
n
um
be
r
of
D
G
un
it
s
are
incre
a
se
d,
t
he
ma
ximum
loa
d
a
b
il
it
y ac
hie
v
e
d
are
m
ore less the sam
e
for pla
cem
e
n
t
of tw
o D
G
uni
ts. H
e
nce
, cons
ide
r
in
g t
h
e
in
sta
l
lat
i
o
n
a
n
d
ma
in
tena
nce
c
o
st,
tw
o
D
G
u
n
i
t
s
w
i
th
4
0
%
p
e
n
e
t
r
at
io
n
le
ve
l
a
r
e
r
eco
m
m
e
nded
for
33-
bu
s
radia
l
d
is
tri
b
utio
n
ne
t
w
or
k.
T
hi
s
re
sul
t
i
s
a
g
a
i
n
co
ns
i
s
ten
t
w
i
th
t
h
e
f
i
n
ding
o
bt
ai
n
e
d
in
[
2
6
]
w
hi
ch
c
onfi
r
ms
the c
a
pa
b
i
li
ty
o
f V
S
CI a
nd th
e va
lue o
f
p
ower
losses ob
ta
i
n
ed
i
n
D
G
pla
cem
ent a
nd s
i
zi
ng.
Ta
b
l
e
3.
Comp
a
riso
n
of
m
a
x
i
m
um
l
oada
bi
l
i
t
y
o
f d
i
ffere
nt
D
G
pe
ne
trat
io
n leve
l
an
d
po
w
e
r
fac
t
or
.
pf
D
G
s
=
1
DGs
=
2
D
Gs
=
3
DG
P
e
n
e
t
r
a
tion
(%)
D
G
P
e
n
e
t
r
a
tion
(%)
D
G
P
e
n
e
tr
a
t
ion
(
%
)
20
4
0
60
8
0
20
4
0
60
8
0
20
40
6
0
80
1
3.
89
4
.
0
6
4.
19
4
.
3
3
.
9
5
4.
25
4
.
52
4.
76
3.
9
4
4
.
2
4
4.
52
4
.
7
7
0.
95
3
.
9
2
4.
12
4
.
2
8
4.
42
4
.
0
1
4.
38
4
.
72
5.
04
4
4.
37
4
.
7
3
5
.
07
0.
9
3.
93
4
.
1
3
4.
3
4.
44
4
.
0
2
4.
4
4.
77
5.
11
4.
0
2
4
.
4
4
.
7
7
5
.
13
0.
85
3.
93
4.
14
4.
3
4.
44
4.
03
4.
42
4.
78
5.
14
4.
0
2
4.
41
4.
79
5.
1
6
0.
8
3.
93
4
.
1
3
4.
3
4.
44
4
.
0
3
4.
42
4
.
78
5.
14
4.
0
2
4
.
4
1
4.
79
5
.
1
6
0.
75
3
.
9
2
4.
13
4
.
2
9
4.
43
4
.
0
2
4.
41
4
.
78
5.
13
4.
0
2
4
.
4
1
4.
79
5
.
1
5
Evaluation Warning : The document was created with Spire.PDF for Python.
ISS
N
:
208
8-
8
6
9
4
I
n
t
J Po
w
Elec
&
Dr
i
Sy
st,
Vo
l. 1
0
,
No
. 3
,
S
e
p
2
019
:
1
317
–
1
3
23
1
322
F
i
g
u
r
e
3
.
C
om
par
i
s
on
o
f
p
ow
er
l
osse
s
for
a
un
it
D
G
plac
ed
a
t
w
e
ak
buse
s
.
4.
CONCLUSION
I
n
t
h
i
s
pa
per
,
a
n
eva
l
ua
tio
n
of
a
v
ol
ta
ge
s
t
a
b
ili
t
y
i
nde
x
for
D
G
plac
em
ent
i
n
r
a
d
ia
l
d
i
s
t
ri
bu
tio
n
ne
t
w
or
k
is
p
r
e
sen
t
ed.
V
S
CI
i
s
use
d
t
o
de
te
r
m
ine
D
G
pl
ac
em
ent
c
a
nd
i
d
a
t
es,
w
h
i
l
e
pow
er
l
osse
s
is
u
se
d
t
o
c
h
o
o
se
t
he
b
es
t
D
G
place
s.
T
h
e
w
e
a
k
buse
s
r
a
nki
ng
b
a
s
ed
on
V
S
CI
g
ive
s
a
l
m
os
t
s
i
milar r
e
su
lt
whe
n co
m
p
ar
e
to
v
o
l
t
a
ge
b
us
es
m
agni
t
ude
s
and
a
l
so
f
in
d
i
n
g
s
i
n
[
2
5
]
.
T
he
r
e
f
o
r
e,
i
t
c
a
n
be
c
onc
l
u
d
e
d
t
h
a
t
V
S
C
I
ca
n
be
u
til
i
z
e
d
a
s
th
e
st
ab
ili
ty
i
nd
i
c
a
t
o
r
o
f
ra
d
i
al
d
ist
r
i
b
uti
o
n
po
we
r
syst
e
m
.
The
study
i
s
c
o
n
d
u
cte
d
o
n
t
h
e
3
3
-
b
us
r
a
dia
l
d
i
s
t
r
ib
ut
io
n
ne
tw
or
k,
a
nd
t
he
r
e
s
u
lts
s
how
t
he
i
m
p
a
c
t
s
o
f
DG,
b
o
th
i
n
t
o
t
a
l
p
o
w
e
r
l
o
s
s
r
e
du
ct
io
n
and
m
a
xim
u
m
l
o
a
d
ab
i
l
i
t
y
impr
ove
me
nt
u
n
d
er
s
tr
e
s
se
d
o
p
e
r
at
io
n.
R
e
s
u
l
ts
s
h
o
w
t
h
a
t
,
with
4
0
%
DG
pe
ne
tra
tio
n
on
l
y
,
pow
er
l
o
s
se
s ca
n
be
r
e
d
uced
u
p t
o
4
8
%
a
n
d
m
a
x
i
m
u
m
loada
b
i
l
i
t
y
of
t
h
e
sy
st
em c
an
i
n
c
re
a
s
e u
p
to
3
0
%
.
F
r
om
a
bove
r
esu
lts,
i
t
c
a
n
a
l
s
o
be
o
bser
ve
d
tha
t
t
he
p
e
r
f
o
r
m
a
n
c
e
o
f
d
if
fe
r
e
nt
num
ber
o
f
D
G
un
i
t
s’
p
la
cem
ent
c
a
n
gi
ve
a
p
p
r
oxim
a
te
l
y
t
he
s
am
e
r
e
sults.
T
h
is
r
esul
t
is
a
ga
in
c
on
si
st
ent
wi
th
t
h
e
f
in
di
ng
s
obt
a
i
n
e
d
in
[
26
]
.
The
r
ef
or
e,
base
d
o
n
r
e
sul
t
s
p
r
ese
n
t
e
d i
n
t
his
pa
p
e
r
,
VS
C
I
is pr
ove
n t
o
be
able
t
o
de
t
e
r
m
ine
t
h
e
w
e
a
k
est
bus i
n
r
a
dia
l
d
is
tr
i
but
i
on
sy
stem
f
or
D
G
pl
a
c
e
m
e
n
t
and
siz
i
n
g
.
ACKNOWLEDGE
ME
N
T
S
The
au
t
h
o
r
s
w
o
u
l
d
l
i
ke
t
o
t
h
ank
M
i
n
i
s
t
r
y
o
f
H
i
g
h
er
E
duc
ati
o
n
(
M
O
H
E
)
of
M
a
l
a
y
si
a
th
r
o
u
gh
a
r
e
se
arc
h
g
ra
n
t
o
f 201
801
12
FR
GS
f
o
r
t
h
e
fi
n
an
ci
al
sup
po
rt t
o
t
h
i
s r
e
search.
REFERE
NC
E
S
[1]
L
.
J
.
Dul
a
u
an
d
M
.
A
brud
ean,
"
H
y
b
ri
d
W
i
n
d
a
nd
S
ol
ar
P
o
w
er
S
y
s
t
e
m,
"
Jo
ur
na
l of
Com
p
u
t
er S
c
ien
ce
&
Co
n
t
rol
Sy
ste
m
s
,
vol.
6(1),
pp
.
3
0
-33
,
M
a
y
2
0
1
3
.
[2]
L
.
I
.
Du
lau
,
M
.
Ab
rudean
a
n
d
D
.
Bi
ca,
"
Eff
ect
s
of
D
is
trib
u
t
ed
G
en
e
r
at
io
n
on
El
ectric
P
o
w
e
r
S
y
stem
s,
"
In P
r
o
cedia
T
ech
nol
og
y
,
v
ol.
12
,
p
p
.
681
-68
6
,
201
4.
[3]
H.
A
.
At
tia,
Z.
H
.
Os
man
,
M
.
E
l
-Sh
i
bin
i
,
an
d
A
.
A
.
Mo
ftah
,
"
A
n
As
sessm
en
t
of
D
istrib
ut
ed
G
enerat
io
n
Im
p
acts
o
n
D
i
strib
u
tio
n N
e
tw
ork
s
u
si
ng
G
l
o
bal
P
e
rf
orm
a
n
ce
Ind
e
x,
"
Nat
u
r
e
an
d
S
c
ien
c
e
,
v
o
l
.
8(9
)
,
pp
.
1
5
0
-
1
5
8,
2
01
0.
[4]
T
.
A
ckerm
a
n,
G. An
d
erss
on
a
nd
L
.
S
o
d
e
r,
"
Dist
rib
u
t
e
d
G
e
nerati
on
:
A
d
e
finiti
on
,
"
El
ectric
P
o
wer S
y
s
t
em Res
e
a
r
ch
,
v
o
l
.
5
7
(
3),
p
p
.
195-2
0
4
,
2
001
.
[5]
W
.
E
l
-
Kh
att
a
m
and
M
.
M
.
A
.
S
alam
a,
"
D
i
st
rib
u
t
e
d
G
e
nerati
on
T
ech
no
log
i
es,
Defi
n
iti
ons
a
n
d
B
en
efi
t
s
,
"
El
ectric
P
o
wer System
R
e
search
,
v
ol.
71
(2),
pp.
1
1
9
-1
28,
20
0
4
.
[6]
R
S
h
a
r
m
a
,
M
.
S
i
n
g
h
a
n
d
D
.
K
.
J
a
i
n
,
"
P
o
w
e
r
S
y
s
t
e
m
S
t
a
b
i
l
i
t
y
A
n
a
l
y
s
i
s
w
ith
L
arg
e
P
en
etrat
i
o
n
o
f
D
i
st
rib
u
t
e
d
G
e
nerati
on
,
"
6t
h
IEEE Power
Indi
a Interna
tional
Conf
erence (P
II
CON),
D
elhi,
2014
.
[7]
D
.
K
han
i
,
A
.
S
.
Yazdan
kh
ah
a
nd
H
.
M.
K
ojabad
i,
"
Im
pacts
of
D
is
t
r
i
bu
te
d
Ge
ne
r
a
tion
s
on
P
owe
r
S
y
s
te
m
Tra
n
sie
n
t
and Voltage
S
ta
bi
l
ity,"
In
t
e
rn
ation
a
l
Jou
r
n
a
l
o
f
El
ectrica
l P
o
wer &
En
ergy
Systems
,
vo
l. 4
3(1
)
,
p
p
. 4
88
-50
0
,
2
0
1
2
.
[8]
I.
K
u
m
arasw
a
my,
S.
T
arakal
yan
i
a
nd
B
.
V
.
P
ras
a
nt
h,
"
Com
p
ari
s
o
n
o
f
V
olt
a
ge
S
tabi
lity
I
ndi
ces
a
nd
i
t
s
En
ha
n
c
e
m
e
n
t
U
s
i
n
g
D
i
st
r
i
bu
te
d
Ge
n
e
r
a
ti
on
,
"
Proceed
in
gs
of
th
e W
o
rl
d Co
ng
ress o
n
E
ngineer
in
g
,
Lon
d
o
n
,
20
16.
[9]
N.
T
.
Linh
a
nd
T
.
T.
C
huong,
"
Voltage
s
tabi
lity
a
nal
y
si
s
of
g
ri
ds
c
on
nect
ed
w
i
n
d
g
e
nerat
o
rs,
"
P
ro
ce
ed
in
gs
o
f
4th
IE
EE
C
onferen
ce Ind
u
s
t
ri
a
l
Elect
ro
ni
cs
a
n
d
A
ppli
catio
n
s
(ICIEA
20
09
),
p
p
.
2
65
7-2
660
,
2
00
9.
[10]
A
.
K
azem
i
and
M
.
S
adeg
hi
,
"D
ist
r
ib
ut
ed
G
en
era
t
io
n
A
l
lo
ca
tio
n
fo
r
Lo
ss
R
ed
uction
a
n
d
V
o
l
t
a
ge
I
m
p
rov
e
m
e
nt,
"
i
n
A
s
i
a
-Pa
c
ific P
o
wer
an
d E
n
er
gy E
n
g
i
neer
in
g
Conf
eren
c
e
,
W
u
han,
2
0
0
9
.
Evaluation Warning : The document was created with Spire.PDF for Python.
Int J
P
o
w
El
e
c
&
D
ri S
yst
IS
S
N
:
2088-
86
94
Inv
e
st
i
g
a
t
i
o
n o
f
di
st
r
i
bu
te
d ge
ner
a
ti
on u
n
its
pl
acem
en
t a
nd
siz
i
n
g
b
a
se
d o
n
vol
t
age
… (Nur Fa
di
l
ah A
b
Aziz)
1
323
[11]
E.
Y
o
u
ssef,
R
.
M
.
E
l
A
z
ab
a
n
d
A
.
M
.
A
m
i
n
,
"
Com
p
arat
iv
e
st
udy
of
v
o
l
tag
e
s
tabi
lity
a
nal
y
sis
f
o
r
renew
a
bl
e
ener
g
y
gri
d
-con
nect
ed
s
ys
tems
u
si
ng
PSS
/E
,
"
So
u
t
heas
t Co
nf
eren
ce
,
F
ort
Lau
d
erdal
e
,
2
015.
[12]
P
.
M
e
h
ta,
P
.
B
h
a
t
t
a
nd
V
.
P
a
nd
ya,
"
O
pt
im
al
s
ele
c
ti
on
o
f
dis
t
ri
b
uted
g
enerati
n
g
u
n
i
t
s
an
d
its
p
l
ace
men
t
f
or
v
o
l
t
a
ge
st
abilit
y
enhan
c
e
m
ent
and
energy l
o
ss
min
imi
zation,
"
A
i
n S
h
a
ms
En
gine
e
r
ing
J
o
u
r
n
a
l
,
201
5
.
[13]
G.
N
annap
a
nen
i
,
T.
M
.
M
a
s
a
ud
an
d
R.
C
h
a
ll
oo,
"
A
com
p
reh
e
n
s
i
v
e
a
n
a
ly
sis
o
f
v
o
l
ta
ge
s
ta
bi
li
ty
i
nd
ic
e
s
i
n
th
e
pres
ence o
f
d
istri
b
u
t
ed
gen
eration,"
IE
EE Con
f
eren
ce on
T
echn
o
l
o
g
i
es for S
u
stai
n
a
bi
lity
(
S
usT
ech),
O
g
d
en
,
2
015
.
[14]
H.
N
ahi
lia
a
nd
M
.
Boudour,
"
Vo
ltage
s
tabi
lity
a
nalysi
s
and
o
p
ti
m
a
l
distri
bu
te
d
g
e
nerato
rs
p
l
acem
ent
s
t
u
dy
on
Al
gerian
p
ow
er
n
etw
o
rk,
"
3r
d
Int
e
rna
t
i
o
n
a
l
Co
nf
e
r
ence on
Co
nt
ro
l
,
En
g
i
n
eeri
n
g
&
In
f
o
rmat
io
n
T
echno
lo
gy
(C
E
I
T
)
,
T
le
mc
e
n
, 2
01
5.
[15]
H
.
W
a
n
g
,
X
.
X
u
,
Z
.
Y
a
n
,
Z
.
Y
a
n
g
,
N
.
F
e
n
g
a
n
d
Y
.
C
u
i
,
"
P
r
o
b
a
b
i
l
i
st
i
c
s
tatic
v
olt
a
ge
s
t
a
b
ility
a
nal
y
sis
cons
idering
th
e
correlat
i
o
n
o
f
wind
p
o
w
er,"
Int
e
rnati
o
na
l
Conf
erenc
e
on
Probabilis
t
i
c Methods App
l
i
e
d
t
o
Power Sy
ste
m
s
(P
MA
P
S
),
Beijin
g
,
2
01
6.
[16]
M
.
M
.
A
m
a
n
,
G
.
B
.
J
a
s
m
o
n
,
H
.
M
o
k
h
l
i
s
a
n
d
A
.
H
.
A
.
B
a
k
a
r
,
"
O
p
t
i
m
al
p
l
acem
e
n
t
an
d
si
zin
g
o
f
a
DG
b
ased
o
n
a
n
e
w
p
o
we
r
sta
b
ili
t
y
in
de
x
a
n
d
li
ne
l
osse
s,"
In
tern
at
io
nal Jo
ur
na
l o
f
E
l
ect
ri
cal
Power
&
E
n
er
gy S
y
stem
s
,
vol.
43(1),
pp
.
1
296
-13
0
4
, 2
012
.
[17]
N.
F
.
Ab
A
ziz,
T
.
K.
A
.
Rah
m
an,
Z
.
Z
a
k
aria,
"
V
ol
tage
s
t
a
bility
pred
icti
on
b
y
usi
n
g
Artif
i
c
i
al
I
mmun
e
L
eas
t
S
q
uare
S
u
p
p
o
r
t
V
e
ct
or
M
ach
in
es
(
AILSVM
)"
IEEE 8th Int
e
r
nati
o
n
a
l Po
wer
En
g
i
neer
in
g
an
d O
p
t
i
m
i
z
a
ti
on
Confer
ence,
PEOCO
, n
o.
68
1
4
5
0
1
,
p
p.
6
13
-
6
1
8
, 2
01
4.
[18]
N.
F
.
Ab
A
ziz,
T
.
K.
A
.
Rah
m
a
n
,
Z
.
Z
ak
aria,
"Reacti
v
e
po
wer
p
l
a
nn
in
g
f
o
r
m
a
x
i
m
u
m
l
o
ad
m
argin
im
p
r
ov
e
m
ent
us
in
g
Fast
A
rtifi
c
ial
Im
m
une
S
up
po
rt
V
ecto
r
M
achi
n
e
(F
AISVM
)
,
"
In
ter
nationa
l Revi
ew of
A
u
t
o
ma
ti
c
Co
ntrol
,
v
o
l.
5
(7
), p
p.
43
6
-
4
4
7
, 20
1
4
.
[19]
N.
F
.
A
b
A
ziz,
T
.
K.
A
.
Rah
m
an
,
Z
.
Z
akaria,
"A
n
ew
t
echn
i
qu
e
f
o
r
m
a
ximu
m
lo
ad
m
argin
est
i
m
a
tio
n
a
n
d
pred
icti
on,
"
AR
PN Jo
ur
nal o
f
E
n
g
i
neer
in
g a
nd Ap
pl
ied
Sc
ien
ces
,
v
o
l
.
2
3
(1
0),
p
p
.
17
56
6-17
57
2,
2
01
5.
[20]
N.
F
.
A.
A
z
i
z,
N
.F
.
A
.,
N.
A
.
R
a
hma
t
,
N
.
A.
,
F
.
M
uh
ammad
-
Suk
k
i,
T
.
K
.
A
.
Rah
m
an
,
Z.
M
.
Yasi
n,
N
.
A.
W
aha
b
,
N.A.
S
alim,
"
A
n
ew
w
eak
a
rea
iden
tificat
ion
m
e
th
od
i
n
power
s
ys
t
e
m
based
on
v
oltag
e
s
tabil
i
t
y
,
"
Jou
r
na
l of
T
e
leco
mmu
ni
cati
on
, Electr
onic
and
Com
puter Engin
eeri
n
g
,
vol.
2
-1
1(9
)
,
pp
.
1
71-177
,
2
01
7.
[21]
J.
B
.
V.
S
u
b
rah
m
anyam
,
P
.
Al
lu
vada,
Bandan
a
,
K.
B
hanu
pri
y
a
an
d
C.
S
h
a
shidhar,
"
Renewab
l
e
E
n
ergy
S
ystems:
Dev
e
lop
m
ent
an
d
Pers
pect
ives
o
f
a
H
y
b
r
id
S
olar-W
ind
S
y
s
t
e
m
,"
En
gi
neer
ing,
T
echn
o
l
o
g
y
&
App
l
i
e
d
S
c
ienc
e
Research
,
v
o
l
.
2(1),
2
01
2.
[22]
A.
S
.
O.
O
g
unj
u
y
ig
be,
T.
R
.
A
y
o
d
el
e
an
d
O.
O
.
Ak
in
o
l
a,
"
Im
pac
t
o
f
d
is
tri
buted
g
enerat
ors
o
n
t
h
e
pow
er
l
o
ss
an
d
vo
lt
age
p
r
o
f
ile
o
f
sub
-
tran
s
m
is
s
i
on
n
etwo
rk,"
Jour
na
l o
f
Electr
i
c
a
l Syst
ems
a
nd Inf
o
r
m
ati
on T
ech
n
o
l
ogy
,
vol.
3(1
)
,
pp
.
9
4-10
7,
2
0
1
6
.
[23]
U.
S
u
ltana,
A.B
.
K
h
a
i
r
u
d
d
in,
M
.
M.
A
man
,
A
.S
.
Mo
kh
t
a
r,
N
.
Zareen
,
"A
r
ev
iew
o
f
o
ptim
um
D
G
pl
ace
m
e
n
t
b
as
ed
on
m
i
n
imi
zati
o
n
o
f
p
ower
l
o
s
s
e
s
and
v
o
l
t
age
st
abili
t
y
en
hancem
e
n
t
o
f
distribu
ti
on
s
y
stem
,
"
R
e
newab
l
e an
d
Su
st
a
i
n
a
b
l
e E
n
e
r
gy
R
eviews
, n
o.
63
, pp
.
3
63
-3
78
,
2
0
1
6
.
[24]
A.
W
azir
an
d
N.
A
rb
ab,
"An
a
ly
sis
and
op
tim
i
zati
o
n
o
f
I
E
E
E
33
b
u
s
radi
al
d
istr
i
b
ut
ed
s
yste
m
using
opti
mization
algorithm,
"
Jo
ur
na
l of
E
m
er
g
i
n
g
Tr
end
s
i
n
Appli
e
d E
ngin
e
er
in
g
,
v
o
l.
1(2
),
p
p.
1
7-2
1
, 2
01
6.
[25]
M.
Ettehadi,
H.
G
hasemi,
S
.
V
a
ez-
Zadeh,
"
Voltage
s
tabili
t
y
-ba
s
e
d
D
G
p
l
acemen
t
i
n
d
ist
r
ib
u
t
i
on
net
w
ork
s
,"
IEEE
Tran
sac
t
io
ns
on
Po
we
r De
liv
e
r
y
,
vo
l.
1
(2)8
,
p
p
.
1
7
1-17
8,
201
3.
[26]
M.
M
.
A
m
an,
G.
B
.
Jasm
on,
A
.
H.
A
.
Bakar
and
H.
M
okh
lis
,
"
A
n
ew
a
pp
roa
c
h
f
o
r
o
p
tim
u
m
s
im
ulta
n
e
ou
s
mul
t
i
-
DG
d
i
s
t
r
ibu
t
ed
g
en
erati
on
Uni
t
s
p
l
acem
ent
and
si
zing
b
as
ed
o
n
m
axi
m
i
z
a
tion
of
s
yst
e
m
loadabil
i
t
y
using
HPSO
(h
yb
rid pa
r
tic
le
s
wa
rm
opt
i
m
izat
i
o
n) algor
ithm,
"
Energy
,
vo
l
.
6
6,
p
p
.
2
0
2
-2
15
,
2014
.
Evaluation Warning : The document was created with Spire.PDF for Python.